Question

How many pounds of nuts worth $1.10 per pound must be mixed with 36 pounds of candy worth $1.60 per pound to produce a par.50 per pound?

Answer 1

To produce a $1.50 per pound mixture, 9 pounds of nuts worth $1.10 per pound must be mixed with 36 pounds of candy worth $1.60 per pound.

Step-by-step explanation:

To find how many pounds of nuts worth $1.10 per pound must be mixed with 36 pounds of candy worth $1.60 per pound to produce a $1.50 per pound mixture, we can use the concept of weighted averages. Let's assume x pounds of nuts need to be mixed with the candy. The value of the nuts is $1.10 per pound, so the total value of the nuts is 1.10x. The value of the candy is $1.60 per pound, so the total value of the candy is 1.60(36). The total weight of the mixture is the sum of the weights of the nuts and candy, which is x + 36 pounds. Setting up the equation:

1.10x + 1.60(36) = 1.50(x + 36)

Solving for x:

1.10x + 57.6 = 1.50x + 54

0.40x = 3.6

x = 9

Therefore, 9 pounds of nuts worth $1.10 per pound must be mixed with 36 pounds of candy worth $1.60 per pound to produce a $1.50 per pound mixture.